大学物理 ›› 2023, Vol. 42 ›› Issue (8): 55-.doi: 10.16854/j.cnki.1000-0712.220422
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张毅，梁兆新
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ZHANG Yi, LIANG Zhao-xin
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摘要： 电子的自旋是没有经典物理对应的纯粹量子特性，其基本性质是自旋空间中的自旋在任意方向上取值为.而找到一个演示电子自旋该性质的可视化例子是量子力学教学的重点和难点.本文通过构造三种不同的旋转算符，利用相似变换把旋转到自旋空间任意方向中的，进而视图化验证自旋本征值取，且比较了三种旋转算符在验证上述自旋基本性质上的优缺点.
关键词: 自旋, 旋转算符, SO(3)群, SU(2)群, 相似变换
Abstract: The spin of an electron is a pure quantum property without the counterpart of the classical physics. Its basic property is that the value of the spin in any direction in the spin space is. Finding a visual example to demonstrate this property of the electron spin is the key and difficult point in quantum mechanics teaching. In this work, the similarity transformation is used to rotate to which represents an arbitrary direction in the spin space by constructing three different rotation operators, and then the eigenvalue of the spin S^n is verified to be . Additionally, this paper shows the advantages and disadvantages of the three rotation operators in verifying the basic properties of the spin.
Key words: spin, rotation operator, group SO(3), group SU(2), similarity transformation
张毅, 梁兆新. 自旋旋转至的相似变换可视化[J]. 大学物理, 2023, 42(8): 55-.
ZHANG Yi, LIANG Zhao-xin. Visualization of similarity transformation with spin rotating to [J]. College Physics, 2023, 42(8): 55-.
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链接本文: https://dxwl.bnu.edu.cn/CN/10.16854/j.cnki.1000-0712.220422
https://dxwl.bnu.edu.cn/CN/Y2023/V42/I8/55
Cited
旋转至
的相似变换可视化
rotating to 
.而找到一个演示电子自旋该性质的可视化例子是量子力学教学的重点和难点.本文通过构造三种不同的旋转算符，利用相似变换把
旋转到自旋空间任意方向中的
，进而视图化验证自旋
本征值取
，且比较了三种旋转算符在验证上述自旋基本性质上的优缺点.